V 2.91 Shrink Wrap Modifer is Not Allowing Target Selection
If you just want a cube with rounded corners, the easiest way is to add a bevel modifier, increase the segments to something like 3 or 4 and then add a Subdivision surface modifier set to something like level 2:

If you want the whole cube to be round (like ballooning out), use a Subdivision Surface Modifier, followed by a Cast Modifier set to cuboid:

If you want the edges and corners rounded (like dice), inset every face slightly, and then add a Subdivision Surface Modifier: